MathsCBSE Class 10 · Standard · Board exam 2023, set 30/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 30(a)

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section C, question 30(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(a) · 3 marks · Short answerPair of Linear Equations in Two Variables

If the system of linear equations $2 x + 3 y = 7$ and $2 a x + (a + b) y = 28$ have infinite number of solutions, then find the values of ' $a$ ' and ' $b$ '.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Recall the ratio condition for coincident lines (infinitely many solutions).

Hint 2

Equate each ratio to $\frac{7}{28} = \frac{1}{4}$ to find $a$ first, then $b$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

For infinitely many solutions, $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$ :
$\frac{2}{2 a} = \frac{3}{a + b} = \frac{7}{28}$
1 mark
$\frac{1}{a} = \frac{1}{4} \Rightarrow a = 4$
1 mark
$\frac{3}{a + b} = \frac{1}{4} \Rightarrow a + b = 12 \Rightarrow b = 12 - 4 = 8$
1 mark

Answer: $a = 4$ , $b = 8$

Where the marks are

Writes the condition $\frac{2}{2 a} = \frac{3}{a + b} = \frac{7}{28}$ (1 mark)
Finds $a = 4$ (1 mark)
Finds $b = 8$ (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
Topic: Graphical Method of Solving Linear Equations

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 30(a)

Hints

Step-by-step solution

Revise the chapter

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